A Collapse Mechanics-Based Criterion for the Optimal Proportioning of Steel Moment Frames Subjected to Earthquakes
Publication: Journal of Structural Engineering
Volume 148, Issue 10
Abstract
Given a certain steel budget, what is the optimal way of distributing it over the height of a steel moment frame building to maximize collapse resistance during earthquakes? An optimality criterion based on the mechanics of collapse of steel moment frame buildings is developed to address this question. The method is used to reproportion the steel moment frames of an existing 18-story steel moment frame building, keeping the total steel tonnage about the same as that of the original building. The response of the reproportioned building to 18 near-source ground motion records from past earthquakes and synthetic ground motion histories at 636 sites in southern California under a simulated 1857-like great San Andreas Fault earthquake is compared with that of the existing building to demonstrate the effectiveness of the methodology. Design tables of optimal beam and column plastic moment distributions are presented for use in the design of 10-, 20-, 30-, and 40-story buildings with 2-bay and 3-bay moment frame configurations.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
Financial support in the form of a summer grant from Manhattan College is gratefully acknowledged. Figs. 9 and 12 were created using Generic Mapping Tools (https://www.generic-mapping-tools.org).
References
AISC. 2017. Steel construction manual. 15th ed. Chicago: AISC.
Alimoradi, A., S. Pezeshk, and C. Foley. 2007. “Probabilistic performance-based optimal design of steel moment-resisting frames II: Applications.” J. Struct. Eng. 133 (6): 767–776. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:6(767).
Arroyo, O., A. V. Osorio, and M. C. Vargas. 2019. “A method to improve the seismic performance of steel moment resisting frames based on eigenfrequency optimization.” Adv. Civ. Eng. 2019: 10. https://doi.org/10.1155/2019/8385342.
ASCE. 2013. Seismic evaluation and retrofit of existing buildings. ASCE 41-13. Reston, VA: ASCE.
ASCE. 2017. Seismic evaluation and retrofit of existing buildings. ASCE 41-17. Reston, VA: ASCE.
Carlson, A. 1999. Three-dimensional nonlinear inelastic analysis of steel moment frame buildings damaged by earthquake excitations. Technical Rep. No. EERL 99-02. Pasadena, CA: Earthquake Engineering Research Laboratory, California Institute of Technology.
Casarotti, E., M. Stupazzini, S. J. Lee, D. Komatitsch, A. Piersanti, and J. Tromp. 2008. “CUBIT and seismic wave propagation based upon the spectral-element method: An advanced unstructured mesher for complex 3D geological media.” In Proc., 16th Int. Meshing Roundtable, edited by M. L. Brewer and D. Marcum, 579–597. Berlin: Springer.
Challa, V. R. M. 1992. Nonlinear seismic behavior of steel planar moment-resisting frames. Technical Rep. No. EERL 92-01. Pasadena, CA: Earthquake Engineering Research Laboratory, California Institute of Technology.
Challa, V. R. M., and J. F. Hall. 1994. “Earthquake collapse analysis of steel frames.” Earthquake Eng. Struct. Dyn. 23 (11): 1199–1218. https://doi.org/10.1002/eqe.4290231104.
Chi, W., S. El-Tawil, G. G. Deierlein, and J. F. Abel. 1998. “Inelastic analyses of a 17-story framed building damaged during Northridge.” Eng. Struct. 20 (4–6): 481–495. https://doi.org/10.1016/S0141-0296(97)00036-9.
FEMA. 2000. Prestandard and commentary for the seismic rehabilitation of buildings. FEMA 356. Washington, DC: FEMA.
Foley, C., S. Pezeshk, and A. Alimoradi. 2007. “Probabilistic performance-based optimal design of steel moment-resisting frames. I: Formulation.” J. Struct. Eng. 133 (6): 757–766. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:6(757).
Fragiadakis, M., and N. D. Lagaros. 2011. “Structural seismic design optimization frameworks: An overview.” Comput. Struct. 89 (11): 1155–1165. https://doi.org/10.1016/j.compstruc.2010.10.021.
Gholizadeh, S., R. Kamyab, and H. Dadashi. 2013. “Performance-based design optimization of steel moment frames.” Int. J. Optim. Civ. Eng. 3 (2): 327–343.
Gong, Y. 2005. “Optimal stiffness distribution of steel moment frames under extreme earthquake loading.” Adv. Struct. Eng. 8 (6): 573–584. https://doi.org/10.1260/136943305776318428.
Hall, J. F. 1995. Parameter study of the response of moment-resisting steel frame buildings to near-source ground motions. Pasadena, CA: Earthquake Engineering Research Laboratory, California Institute of Technology.
Hall, J. F. 1998. “Seismic response of steel frame buildings to near-source ground motions.” Earthquake Eng. Struct. Dyn. 27 (12): 1445–1464. https://doi.org/10.1002/(SICI)1096-9845(199812)27:12%3C1445::AID-EQE794%3E3.0.CO;2-C.
Hall, J. F., and V. R. M. Challa. 1995. “Beam-column modeling.” J. Eng. Mech. 121 (12): 1284–1291. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:12(1284).
Hauksson, E. 2000. “Crustal structure and seismicity distribution adjacent to the Pacific and North American plate boundary in Southern California.” J. Geophys. Res. 105 (B6): 13875–13903. https://doi.org/10.1029/2000JB900016.
Kaufmann, E. J., M. Xue, L.-W. Lu, and J. W. Fisher. 1996. “Achieving ductile behavior of moment connections.” Mod. Steel Constr. 36 (1): 30–39.
Kaveh, A., M. Z. Kabir, and M. Bohlool. 2020. “Optimum design of three-dimensional steel frames with prismatic and non-prismatic elements.” Eng. Comput. 36 (3): 1011–1027. https://doi.org/10.1007/s00366-019-00746-9.
Kaveh, A., M. Kalateh-Ahani, and M. Fahimi-Farzam. 2014. “Life-cycle cost optimization of steel moment-frame structures: Performance-based seismic design approach.” Earthquakes Struct. 7 (3): 271–294. https://doi.org/10.12989/eas.2014.7.3.271.
Kellogg, L. 2011. Computational infrastructure for geodynamics. Davis, CA: Univ. of California.
Komatitsch, D., Q. Liu, J. Tromp, P. Süss, C. Stidham, and J. H. Shaw. 2004. “Simulations of ground motion in the Los Angeles basin based upon the spectral element method.” Bull. Seismol. Soc. Am. 94 (1): 187–206. https://doi.org/10.1785/0120030077.
Komatitsch, D., and J. Tromp. 1999. “Introduction to the spectral element method for three-dimensional seismic wave propagation.” Geophys. J. Int. 139 (3): 806–822. https://doi.org/10.1046/j.1365-246x.1999.00967.x.
Krishnan, S. 2003a. FRAME3D: A program for three-dimensional nonlinear time-history analysis of steel buildings: User guide. Pasadena, CA: Earthquake Engineering Research Laboratory, California Institute of Technology.
Krishnan, S. 2003b. Three-dimensional nonlinear analysis of tall irregular steel buildings subject to strong ground motion. Pasadena, CA: Earthquake Engineering Research Laboratory, California Institute of Technology.
Krishnan, S. 2007. “Case studies of damage to 19-storey irregular steel moment frame buildings under near-source ground motion.” Earthquake Eng. Struct. Dyn. 36 (7): 861–885. https://doi.org/10.1002/eqe.657.
Krishnan, S. 2009. FRAME3D V2.0 - A program for the three dimensional nonlinear analysis of steel buildings: User guide. Pasadena, CA: California Institute of Technology.
Krishnan, S., and J. F. Hall. 2006a. “Modeling steel frame buildings in three dimensions: Part I: Panel zone and plastic hinge beam elements.” J. Eng. Mech. 132 (4): 345–358. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:4(345).
Krishnan, S., and J. F. Hall. 2006b. “Modeling steel frame buildings in three dimensions: Part II: Elastofiber beam element and examples.” J. Eng. Mech. 132 (4): 359–374. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:4(359).
Krishnan, S., C. Ji, D. Komatitsch, and J. Tromp. 2005. Performance of 18-story steel moment frame buildings during a large San Andreas earthquake: A Southern California-wide end-to-end simulation. Pasadena, CA: Earthquake Engineering Research Laboratory, California Institute of Technology.
Krishnan, S., C. Ji, D. Komatitsch, and J. Tromp. 2006a. “Case studies of damage to tall steel moment frame buildings in southern California during large San Andreas earthquakes.” Bull. Seismol. Soc. Am. 96 (4): 1523–1537. https://doi.org/10.1785/0120050145.
Krishnan, S., C. Ji, D. Komatitsch, and J. Tromp. 2006b. “Performance of two 18-story steel moment frame buildings in southern California during two large simulated San Andreas earthquakes.” Earthquake Spectra 22 (4): 1035–1061. https://doi.org/10.1193/1.2360698.
Krishnan, S., and M. Muto. 2012. “Mechanism of collapse of tall steel moment frame buildings under earthquake excitation.” J. Struct. Eng. 138 (11): 1361–1387. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000573.
Krishnan, S., and M. Muto. 2013. “Sensitivity of the earthquake response of tall steel moment frame buildings to ground motion features.” J. Earthquake Eng. 17 (5): 673–698. https://doi.org/10.1080/13632469.2013.771587.
Lagaros, N. D., and M. Fragiadakis. 2007. “Robust performance-based design optimization of steel moment resisting frames.” J. Earthquake Eng. 11 (5): 752–772. https://doi.org/10.1080/13632460601087229.
Lagaros, N. D., A. T. Garavelas, and M. Papadrakakis. 2008. “Innovative seismic design optimization with reliability constraints.” Comput. Methods Appl. Mech. Eng. 198 (1): 28–41. https://doi.org/10.1016/j.cma.2007.12.025.
Lin, G., P. M. Shearer, E. Hauksson, and C. H. Thurber. 2007. “A three-dimensional crustal seismic velocity model for Southern California from a composite event method.” J. Geophys. Res. 112 (B11): B11306. https://doi.org/10.1029/2007JB004977.
Liu, M., S. A. Burns, and Y. Wen. 2004. “Multiobjective optimization for performance-based seismic design of steel moment frame structures.” Earthquake Eng. Struct. Dyn. 34 (3): 289–306. https://doi.org/10.1002/eqe.426.
Liu, M., S. A. Burns, and Y. Wen. 2006. “Genetic algorithm based construction-conscious minimum weight design of seismic steel moment-resisting frames.” J. Struct. Eng. 132 (1): 50–58. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:1(50).
Liu, Z., S. Atamturktur, and C. Juang. 2013. “Performance based robust design optimization of steel moment resisting frames.” J. Constr. Steel Res. 89 (Oct): 165–174. https://doi.org/10.1016/j.jcsr.2013.07.011.
McKinstray, R., J. Lim, T. Tanyimboh, D. Phan, and W. Sha. 2015. “Optimal design of long-span steel portal frames using fabricated beams.” J. Constr. Steel Res. 104 (Jan): 104–114. https://doi.org/10.1016/j.jcsr.2014.10.010.
Papadrakakis, M., N. Lagaros, and V. Plevris. 2001. “Optimum design of space frames under seismic loading.” Int. J. Struct. Stab. Dyn. 1 (1): 105–123. https://doi.org/10.1142/S0219455401000093.
Plesch, A., C. Tape, R. Graves, J. H. Shaw, P. Small, and G. Ely. 2011. “Updates for the CVM-H including new representations of the offshore Santa Maria and San Bernardino basins and a new Moho surface.” In Proc., SCEC 2011 Annual Meeting. Los Angeles: Southern California Earthquake Center.
Prindle, K., and T. Tanimoto. 2006. “Teleseismic surface wave study for -wave velocity structure under an array: Southern California.” Geophys. J. Int. 166 (2): 601–621. https://doi.org/10.1111/j.1365-246X.2006.02947.x.
Rojas, H., C. Foley, and S. Pezeshk. 2011. “Risk-based seismic design for optimal structural and nonstructural system performance.” Earthquake Spectra 27 (3): 857–880. https://doi.org/10.1193/1.3609877.
SAC (Structural Engineers Association of California). 1995. Analytical and field investigations of buildings affected by the Northridge earthquake of January 17, 1994: Part 1. Sacramento, CA: SAC.
Sandia National Laboratory. 2011. CUBIT: Geometry and mesh generation toolkit. Albuquerque, NM: Sandia National Laboratory.
Siriki, H., R. Mourhatch, and S. Krishnan. 2021. “Limit state exceedance probabilities of building performance under earthquake excitation using rupture-to-rafters simulations.” J. Earthquake Eng. 25 (12): 2495–2536. https://doi.org/10.1080/13632469.2019.1628124.
Süss, M. P., and J. H. Shaw. 2003. “P-wave seismic velocity structure derived from sonic logs and industry reflection data in the Los Angeles basin, California.” J. Geophys. Res. 108 (B3): 2170. https://doi.org/10.1029/2001JB001628.
Tape, C., Q. Liu, A. Maggi, and J. Tromp. 2009. “Adjoint tomography of the southern California crust.” Science 325 (5943): 988–992. https://doi.org/10.1126/science.1175298.
Tape, C., Q. Liu, A. Maggi, and J. Tromp. 2010. “Seismic tomography of the southern California rust based on spectral-element and adjoint methods.” Geophys. J. Int. 180 (1): 433–462. https://doi.org/10.1111/j.1365-246X.2009.04429.x.
Tehranizadeh, M., and A. Moshref. 2011. “Performance-based optimization of steel moment resisting frames.” Sci. Iran. 18 (2): 198–204. https://doi.org/10.1016/j.scient.2011.03.029.
Tsompanakis, Y., and M. Papadrakakis. 2004. “Large-scale reliability-based structural optimization.” Struct. Multidiscip. Optim. 26 (6): 429–440. https://doi.org/10.1007/s00158-003-0369-5.
Wu, Y.-M., T.-L. Teng, T.-C. Shin, and N.-C. Hsiao. 2003. “Relationship between peak ground acceleration, peak ground velocity, and intensity in Taiwan.” Bull. Seismol. Soc. Am. 93 (1): 386–396. https://doi.org/10.1785/0120020097.
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Published In
Journal of Structural Engineering
Volume 148 • Issue 10 • October 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Oct 23, 2021
Accepted: Mar 21, 2022
Published online: Jul 22, 2022
Published in print: Oct 1, 2022
Discussion open until: Dec 22, 2022
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